Recent Advances in Approximation and Potential Theory

Over the course of his distinguished career, Edward Saff has made a number of groundbreaking contributions in the fields of approximation theory, potential theory, and complex analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Ed Saff at 80: Career and Distinguished Scientific Contributions. - Exponential bases on modified domains. - Positive definite singular kernels on two-point homogeneous spaces. - H ormander and Bernhardsson s extremal function I. - Absolute Minima of Potentials of a Certain Class of Spherical Designs. - Logarithmic and Riesz Energy on the Sphere: Better Bounds via elementary Methods. - Energy of codes with forbidden distances in 48 dimensions. - Frequency-dependent stability for Gabor frames. - A nonnegative even kernel arising from extremal sine polynomials. - The number of real zeros of polynomials with constrained coefficients. - Approximate orthogonality, Bourgain s pinned distance theorem, and exponential frames. - Application of Sparse Grids to Approximation and Optimization. - Shape preserving approximation of periodic functions A survey. - Spaces of trigonometric series and the Wiener algebra. - Variational Conditions on Extremal Orthonormal Polynomials for Restricted Measures. - Behavior of bounded solutions, ( , ), to the heat equation in R × (0, )as . - Weighted equilibrium and the flow of derivatives of polynomials. - A linear programming bound in a sign-alternating case. - Approximation by Fourier sums on the classes of generalized Poisson integrals. - On Linear Spaces with Ideal Complements. - On Analytic Functions with Taylor Coefficients Taken from a Finite Set.